1. ## Calculus Help

I need help finding the second derivative and critical numbers of this function.

$\displaystyle f(x)=x^{2/3}(x-3)^{1/3}$
I get a first derivative of
$\displaystyle f'(x)=2/9x^{1/3}(x-3)^{1/3}+1/3x^{2/3}$
and a second derivative of
$\displaystyle f"(x)=(x-3)^{1/3}+{2/9}x^{1/3}$
but i dont think this is right because I cant find the critical numbers

2. Originally Posted by jjedlicka
I need help finding the second derivative and critical numbers of this function.

$\displaystyle f(x)=x^{2/3}(x-3)^{1/3}$
I get a first derivative of
$\displaystyle f'(x)=2/9x^{1/3}(x-3)^{1/3}+1/3x^{2/3}$
and a second derivative of
$\displaystyle f"(x)=(x-3)^{1/3}+{2/9}x^{1/3}$
but i dont think this is right because I cant find the critical numbers
indeed, there are no critical points. however, you're derivatives are not correct. you need to use the power rule here. it seems you attempted to, but it was not properly executed.

recall: $\displaystyle \frac d{dx}f(x)g(x) = f'(x)g(x) + f(x)g'(x)$